Finite Group Databasebeta

← C2×#13080380 #15629952

Subgroups — C2×#13080380 #15629952

Order 2816.

2704 conjugacy classes of subgroups.

The subgroup lattice has 1174 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623367C211yesmaximal, characteristic, complemented
2C2×#10623301C211yesmaximal, characteristic, complemented
3C2×#10623366C211yesmaximal, characteristic, complemented
4#13080380C2116yesmaximal, direct product factor
5C2×#10622767C211yesmaximal, characteristic, complemented
6C2×#10622812C211yesmaximal, characteristic, complemented
7C2×#10622773C211yesmaximal, characteristic, complemented
8C2×#10622754C211yesmaximal, characteristic, complemented
9C2×#10622813C211yesmaximal, characteristic, complemented
10C2×#10622814C211yesmaximal, characteristic, complemented
11C2×#10622855C211yesmaximal, characteristic, complemented
12C2×#10622854C211yesmaximal, characteristic, complemented
13C2×#10622811C211yesmaximal, characteristic, complemented
14C2×#10622810C211yesmaximal, characteristic, complemented
15C2×#10622758C211yesmaximal, characteristic, complemented
16C2×C11×#576C211yesmaximal, characteristic, complemented
17C2×C11×H(5,𝔽2)C2211yescharacteristic
18C2×C11×H(5,𝔽2)C2211yescharacteristic, complemented
19C2×#67043C2211yescharacteristic, complemented
20C2×#67042C2211yescharacteristic, complemented
21C11×#576—24no—
22C11×#576C2218yescomplemented
23C2×C11×AGL(1,ℤ/8)—21no—
24C2×C11×AGL(1,ℤ/8)—21no—
25C2×C11×AGL(1,ℤ/8)C2211yescharacteristic
26C2×C11×AGL(1,ℤ/8)C2211yescharacteristic, complemented
27C2×C11×#135—21no—
28C2×C11×#135C2211yescharacteristic
29C22×C11×D8—21no—
30C22×C11×D8C2211yescharacteristic, complemented
31C2×C11×#131C2211yescharacteristic, complemented
32#10623367—24no—
33#10623367C2218yescomplemented
34#10623366—24no—
35#10623366C2218yescomplemented
36C2×#67004—21no—
37C2×#67004C2211yescharacteristic, complemented
38C2×#67004C2211yescharacteristic, complemented
39C2×#67003—21no—
40C2×#67003—21no—
41C2×#67003C2211yescharacteristic
42C2×#67002—21no—
43C2×#67002C2211yescharacteristic
44C2×#67002C2211yescharacteristic, complemented
45C2×#67001C2211yescharacteristic, complemented
46C2×#67001C2211yescharacteristic, complemented
47C2×#66993C2211yescharacteristic, complemented
48C2×#66989C2211yescharacteristic, complemented
49C22×#4324—21no—
50C22×#4324C2211yescharacteristic, complemented
51C2×#66985—21no—
52C2×#66985—21no—
53C2×#66985C2211yescharacteristic, complemented
54C2×#66985C2211yescharacteristic, complemented
55C22×#4323—21no—
56C22×#4323C2211yescharacteristic, complemented
57#10623301—24no—
58#10623301C2218yescomplemented
59C2×#66971—21no—
60C2×#66969—21no—
61C2×SD16×D11—21no—
62C2×#66964—21no—
63C22×#4314C2211yescharacteristic, complemented
64C2×#66954C2211yescharacteristic, complemented
65#10622855C2218yescomplemented
66#10622854C2218yescomplemented
67C2×#66901C2211yescharacteristic, complemented
68C2×#66901C2211yescharacteristic, complemented
69C2×#66901C2211yescharacteristic, complemented
70C2×#66897C2211yescharacteristic, complemented
71C2×#66897C2211yescharacteristic, complemented
72#10622814C2218yescomplemented
73#10622813C2218yescomplemented
74#10622812C2218yescomplemented
75#10622811C2218yescomplemented
76#10622810C2218yescomplemented
77#10622773C2218yescomplemented
78#10622767C2218yescomplemented
79#10622758C2218yescomplemented
80#10622754C2218yescomplemented
81C2×#66889C2211yescharacteristic, complemented
82C2×#66888C2211yescharacteristic, complemented
83C2×#66887C2211yescharacteristic, complemented
84C2×#66886C2211yescharacteristic, complemented
85C2×#66883C2211yescharacteristic, complemented
86C2×#66879C2211yescharacteristic, complemented
87C11×H(5,𝔽2)—22no—
88C11×H(5,𝔽2)—22no—
89C11×H(5,𝔽2)—22no—
90C11×H(5,𝔽2)—22no—
91C11×H(5,𝔽2)—41no—
92C11×H(5,𝔽2)—41no—
93C11×H(5,𝔽2)C2314yes—
94C11×H(5,𝔽2)C2314yescomplemented
95C2×C11×#41—21no—
96C2×C11×#41—21no—
97C2×C11×#41—21no—
98C2×C11×#41—21no—
99C2×C11×#41C2311yescharacteristic
100C2×C11×#41C2311yescharacteristic
101C2×C11×#41C2311yescharacteristic
102C22×D4×C11—21no—
103C22×D4×C11—21no—
104C22×D4×C11—21no—
105C22×D4×C11—21no—
106C22×D4×C11—41no—
107C22×D4×C11—41no—
108C22×D4×C11C2311yescharacteristic
109C22×D4×C11C2311yescharacteristic
110C22×C22⋊D11—41no—
111#67043—22no—
112#67043—22no—
113#67043—41no—
114#67043C2314yescomplemented
115#67042—22no—
116#67042—22no—
117#67042—41no—
118#67042C2314yescomplemented
119C2×#4343—21no—
120C2×Q8×D11—21no—
121C2×#4341—21no—
122C2×#4341—41no—
123C2×D4×D11—21no—
124C2×D4×D11—41no—
125C2×#4339—21no—
126C2×#4339—21no—
127C2×#4339C2311yescharacteristic
128C22×D44—21no—
129C22×D44C2311yescharacteristic
130C22×Dic22—21no—
131C22×Dic22C2311yescharacteristic
132C11×AGL(1,ℤ/8)—22no—
133C11×AGL(1,ℤ/8)—22no—
134C11×AGL(1,ℤ/8)—28no—
135C11×AGL(1,ℤ/8)—28no—
136C11×AGL(1,ℤ/8)C2314yes—
137C11×AGL(1,ℤ/8)C2314yescomplemented
138C11×#135—28no—
139C11×#135D414yescomplemented
140C11×#135C2314yes—
141C2×C11×Q16D411yescharacteristic, complemented
142C2×C11×SD16—21no—
143C2×C11×SD16—21no—
144C2×C11×SD16D411yescharacteristic, complemented
145C2×C11×SD16D411yescharacteristic, complemented
146C2×C11×D8—21no—
147C2×C11×D8—21no—
148C2×C11×D8—28no—
149C2×C11×D8—21no—
150C2×C11×D8—21no—
151C2×C11×D8—22no—
152C2×C11×D8D411yescharacteristic, complemented
153C2×C11×D8C2314yescomplemented
154C11×#131—22no—
155C11×#131C2314yescomplemented
156C2×C11×M16—21no—
157C2×C11×M16C2311yescharacteristic
158C22×C8×C11—21no—
159C22×C8×C11C2311yescharacteristic
160C2×C22⋊Dic11—41no—
161#67004—22no—
162#67004—22no—
163#67004—28no—
164#67004C2314yescomplemented
165#67004C2314yescomplemented
166#67003—28no—
167#67003—28no—
168#67003D414yescomplemented
169#67003C2314yes—
170#67002—22no—
171#67002—22no—
172#67002—28no—
173#67002C2314yes—
174#67002C2314yescomplemented
175#67001—22no—
176#67001—22no—
177#67001C2314yescomplemented
178#67001C2314yescomplemented
179C2×#4326—21no—
180C2×#4326—21no—
181C2×#4326D411yescharacteristic, complemented
182C2×#4325—21no—
183C2×#4325—21no—
184C2×#4325D411yescharacteristic, complemented
185#66993—41no—
186#66993C2314yescomplemented
187#66989—41no—
188#66989C2314yescomplemented
189C2×#4324—21no—
190C2×#4324—21no—
191C2×#4324—21no—
192C2×#4324—21no—
193C2×#4324—28no—
194C2×#4324—21no—
195C2×#4324—21no—
196C2×#4324—22no—
197C2×#4324D411yescharacteristic, complemented
198C2×#4324C2314yescomplemented
199#66985—22no—
200#66985—22no—
201#66985—28no—
202#66985—28no—
203#66985C2314yescomplemented
204#66985C2314yescomplemented
205C2×#4323—21no—
206C2×#4323—21no—
207C2×#4323—21no—
208C2×#4323—21no—
209C2×#4323—28no—
210C2×#4323—21no—
211C2×#4323—21no—
212C2×#4323—22no—
213C2×#4323D411yescharacteristic, complemented
214C2×#4323C2314yescomplemented
215C2×C4×Dic11C2311yescharacteristic
216C2×#4318—21no—
217C2×#4318—21no—
218C2×#4318C2311yescharacteristic
219C2×#4318C2311yescharacteristic
220C2×#4318C2311yescharacteristic
221C22×C11⋊C8—21no—
222C22×C11⋊C8—21no—
223C22×C11⋊C8C2311yescharacteristic
224#66971—28no—
225#66969—28no—
226SD16×D11—28no—
227#66964—28no—
228C2×#4314—21no—
229C2×#4314—21no—
230C2×#4314—22no—
231C2×#4314C2314yescomplemented
232#66954—22no—
233#66954C2314yescomplemented
234C2×#4313—21no—
235C2×C8×D11—21no—
236#66901C2314yescomplemented
237#66901C2314yescomplemented
238#66901C2314yescomplemented
239#66897C2314yescomplemented
240#66897C2314yescomplemented
241#66889C2314yescomplemented
242#66888C2314yescomplemented
243#66887C2314yescomplemented
244#66886C2314yescomplemented
245#66883C2314yescomplemented
246#66879C2314yescomplemented
247C2×#3288—111nomaximal, Sylow
248C24×C11—21no—
249C24×C11—21no—
250C24×C11—41no—
251C24×C11—41no—
252C23×D11—21no—
253C23×D11—41no—
254C11×#41—21no—
255C11×#41—21no—
256C11×#41—21no—
257C11×#41—21no—
258C11×#41—21no—
259C11×#41—21no—
260C11×#41—24no—
261C11×#41—24no—
262C11×#41—24no—
263C11×#41—24no—
264C11×#41—42no—
265C11×#41—42no—
266C11×#41—42no—
267C11×#41—42no—
268C11×#41C2×D412yes—
269C11×#41C2×D412yes—
270C11×#41C2×D412yes—
271C11×#41C2412yes—
272C11×#41C2412yes—
273C11×#41C2412yes—
274C2×Q8×C11C2×D411yescharacteristic
275C2×Q8×C11C2×D411yescharacteristic
276C2×Q8×C11C2×D411yescharacteristic
277C2×D4×C11—21no—
278C2×D4×C11—21no—
279C2×D4×C11—21no—
280C2×D4×C11—24no—
281C2×D4×C11—24no—
282C2×D4×C11—24no—
283C2×D4×C11—24no—
284C2×D4×C11—21no—
285C2×D4×C11—21no—
286C2×D4×C11—21no—
287C2×D4×C11—21no—
288C2×D4×C11—21no—
289C2×D4×C11—21no—
290C2×D4×C11—21no—
291C2×D4×C11—21no—
292C2×D4×C11—21no—
293C2×D4×C11—21no—
294C2×D4×C11—42no—
295C2×D4×C11—42no—
296C2×D4×C11—42no—
297C2×D4×C11—42no—
298C2×D4×C11—41no—
299C2×D4×C11—41no—
300C2×D4×C11—41no—
301C2×D4×C11—41no—
302C2×D4×C11—44no—
303C2×D4×C11—44no—
304C2×D4×C11—44no—
305C2×D4×C11—44no—
306C2×D4×C11C2×D411yescharacteristic
307C2×D4×C11C2×D411yescharacteristic
308C2×D4×C11C2×D411yescharacteristic
309C2×D4×C11C2412yes—
310C2×D4×C11C2412yes—
311C22×C4×C11—21no—
312C22×C4×C11—21no—
313C22×C4×C11—21no—
314C22×C4×C11—41no—
315C22×C4×C11—41no—
316C22×C4×C11C2411yescharacteristic
317C2×C22⋊D11—21no—
318C2×C22⋊D11—44no—
319C2×C22⋊D11—41no—
320C2×C22⋊D11—41no—
321C2×C22⋊D11—84no—
322C22×Dic11—21no—
323C22×Dic11—21no—
324C22×Dic11—41no—
325#4343—24no—
326#4343—42no—
327Q8×D11—24no—
328Q8×D11—42no—
329#4341—24no—
330#4341—42no—
331#4341—44no—
332#4341—44no—
333D4×D11—24no—
334D4×D11—44no—
335D4×D11—42no—
336D4×D11—44no—
337#4339—24no—
338#4339—24no—
339#4339—21no—
340#4339—21no—
341#4339—42no—
342#4339—42no—
343#4339C2×D412yes—
344#4339C2412yes—
345C2×D44—24no—
346C2×D44—21no—
347C2×D44—21no—
348C2×D44—21no—
349C2×D44—21no—
350C2×D44—21no—
351C2×D44—41no—
352C2×D44—42no—
353C2×D44C2×D411yescharacteristic
354C2×D44C2412yes—
355C2×C4×D11—21no—
356C2×C4×D11—41no—
357C2×C4×D11—41no—
358C2×Dic22—24no—
359C2×Dic22—21no—
360C2×Dic22—21no—
361C2×Dic22—21no—
362C2×Dic22—21no—
363C2×Dic22—21no—
364C2×Dic22—42no—
365C2×Dic22—41no—
366C2×Dic22C2×D411yescharacteristic
367C2×Dic22C2412yes—
368C11×Q16C2×D414yescomplemented
369C11×SD16—24no—
370C11×SD16—24no—
371C11×SD16C2×D414yescomplemented
372C11×SD16C2×D414yescomplemented
373C11×D8—24no—
374C11×D8—24no—
375C11×D8—24no—
376C11×D8—24no—
377C11×D8C2×D414yescomplemented
378C11×M16—24no—
379C11×M16—21no—
380C11×M16C2412yes—
381C2×C8×C11—24no—
382C2×C8×C11—21no—
383C2×C8×C11C2×D411yescharacteristic
384C2×C8×C11C2×D411yescharacteristic
385C2×C8×C11C2×D412yes—
386C2×C8×C11C2412yes—
387C22⋊Dic11—44no—
388#4326—24no—
389#4326—24no—
390#4326C2×D414yescomplemented
391#4325—24no—
392#4325—24no—
393#4325C2×D414yescomplemented
394#4324—24no—
395#4324—24no—
396#4324—24no—
397#4324—24no—
398#4324—24no—
399#4324—24no—
400#4324C2×D414yescomplemented
401#4323—24no—
402#4323—24no—
403#4323—24no—
404#4323—24no—
405#4323—24no—
406#4323—24no—
407#4323C2×D414yescomplemented
408C4×Dic11—21no—
409C4×Dic11C2412yes—
410#4318—24no—
411#4318—24no—
412#4318—21no—
413#4318—21no—
414#4318—21no—
415#4318C2412yes—
416#4318C2412yes—
417#4318C2412yes—
418C2×C11⋊C8—24no—
419C2×C11⋊C8—24no—
420C2×C11⋊C8—21no—
421C2×C11⋊C8—21no—
422C2×C11⋊C8—21no—
423C2×C11⋊C8C2×D411yescharacteristic
424C2×C11⋊C8C2×D411yescharacteristic
425C2×C11⋊C8C2×D412yes—
426C2×C11⋊C8C2412yes—
427#4314—24no—
428#4314—24no—
429#4313—24no—
430C8×D11—24no—
431C2×#577—111no—
432C2×#577—111no—
433C2×#576—111no—
434C2×#576D1111yescharacteristic, complemented
435#3288—1116no—
436C2×#496—111no—
437C2×#472—111no—
438C2×#472—111no—
439C2×#471—111no—
440C2×#471—111no—
441C2×#454—111no—
442C2×#455—111no—
443C2×#453—111no—
444C2×#453—111no—
445C2×#444—111no—
446C2×#444—111no—
447C23×C11—21no—
448C23×C11—21no—
449C23×C11—21no—
450C23×C11—22no—
451C23×C11—22no—
452C23×C11—44no—
453C23×C11—44no—
454C23×C11—41no—
455C23×C11—41no—
456C23×C11—41no—
457C23×C11—41no—
458C23×C11—82no—
459C23×C11—82no—
460C23×C11—162no—
461C23×C11—162no—
462C23×C11H(5,𝔽2)11yescharacteristic
463C22×D11—21no—
464C22×D11—22no—
465C22×D11—44no—
466C22×D11—41no—
467C22×D11—41no—
468C22×D11—82no—
469C22×D11—162no—
470Q8×C11—21no—
471Q8×C11—21no—
472Q8×C11—21no—
473Q8×C11C22×D412yes—
474Q8×C11C22×D412yes—
475Q8×C11C22×D412yes—
476D4×C11—22no—
477D4×C11—22no—
478D4×C11—22no—
479D4×C11—22no—
480D4×C11—22no—
481D4×C11—22no—
482D4×C11—21no—
483D4×C11—21no—
484D4×C11—21no—
485D4×C11—22no—
486D4×C11—22no—
487D4×C11—22no—
488D4×C11—22no—
489D4×C11—44no—
490D4×C11—44no—
491D4×C11—44no—
492D4×C11—44no—
493D4×C11—41no—
494D4×C11—41no—
495D4×C11—41no—
496D4×C11—41no—
497D4×C11C22×D412yes—
498D4×C11C22×D412yes—
499D4×C11C22×D412yes—
500C2×C4×C11—21no—
501C2×C4×C11—21no—
502C2×C4×C11—21no—
503C2×C4×C11—22no—
504C2×C4×C11—22no—
505C2×C4×C11—22no—
506C2×C4×C11—22no—
507C2×C4×C11—22no—
508C2×C4×C11—22no—
509C2×C4×C11—44no—
510C2×C4×C11—44no—
511C2×C4×C11C22×D411yescharacteristic
512C2×C4×C11C22×D411yescharacteristic
513C2×C4×C11C22×D411yescharacteristic
514C2×C4×C11C22×D411yescharacteristic
515C2×C4×C11H(5,𝔽2)11yescharacteristic
516C2×C4×C11C2511yescharacteristic
517C22⋊D11—22no—
518C22⋊D11—22no—
519C22⋊D11—44no—
520C22⋊D11—44no—
521C22⋊D11—88no—
522C2×Dic11—21no—
523C2×Dic11—22no—
524C2×Dic11—22no—
525C2×Dic11—44no—
526C2×Dic11—42no—
527C2×Dic11—41no—
528C2×Dic11—41no—
529D44—21no—
530D44—22no—
531D44—22no—
532D44—44no—
533D44—41no—
534D44—41no—
535D44C22×D412yes—
536C4×D11—22no—
537C4×D11—22no—
538C4×D11—44no—
539C4×D11—44no—
540Dic22—21no—
541Dic22—22no—
542Dic22—22no—
543Dic22—44no—
544Dic22—41no—
545Dic22—41no—
546Dic22C22×D412yes—
547C8×C11—22no—
548C8×C11C22×D412yes—
549C8×C11C22×D412yes—
550C11⋊C8—22no—
551C11⋊C8—22no—
552C11⋊C8—22no—
553C11⋊C8C22×D412yes—
554C11⋊C8C22×D412yes—
555C2×2−1+4—111no—
556C2×H(5,𝔽2)—111no—
557C2×H(5,𝔽2)C2×D1111yescharacteristic
558C2×H(5,𝔽2)C2×D1111yescharacteristic, complemented
559#577—118no—
560#577—118no—
561#577—224no—
562#577—224no—
563#576—24no—
564#576—118no—
565#576—224no—
566#576C2×D1118yescomplemented
567C2×#137—111no—
568C2×#137—111no—
569C2×#137—221no—
570C2×#137—221no—
571C2×AGL(1,ℤ/8)—21no—
572C2×AGL(1,ℤ/8)—21no—
573C2×AGL(1,ℤ/8)—111no—
574C2×AGL(1,ℤ/8)—111no—
575C2×AGL(1,ℤ/8)—111no—
576C2×AGL(1,ℤ/8)—111no—
577C2×AGL(1,ℤ/8)—221no—
578C2×AGL(1,ℤ/8)—221no—
579C2×AGL(1,ℤ/8)—221no—
580C2×AGL(1,ℤ/8)—221no—
581C2×AGL(1,ℤ/8)C2×D1111yescharacteristic
582C2×AGL(1,ℤ/8)C2×D1111yescharacteristic, complemented
583C2×#135—21no—
584C2×#135—111no—
585C2×#135—221no—
586C2×#135—221no—
587C2×#135—221no—
588C2×#135C2×D1111yescharacteristic
589C22×SD16—111no—
590C22×SD16—111no—
591C22×SD16—221no—
592C22×SD16—221no—
593C22×D8—21no—
594C22×D8—111no—
595C22×D8—221no—
596C22×D8C2×D1111yescharacteristic, complemented
597C2×#131—111no—
598C2×#131—111no—
599C2×#131—111no—
600C2×#131C2×D1111yescharacteristic, complemented
601C2×#127—111no—
602C2×#124—111no—
603#496—118no—
604#472—118no—
605#472—118no—
606#471—118no—
607#471—118no—
608#455—118no—
609#454—118no—
610#453—118no—
611#453—118no—
612#444—118no—
613#444—118no—
614C2×#108—111no—
615C2×#108—111no—
616C2×#104—111no—
617C2×#104—111no—
618C2×#104—111no—
619C2×#104—111no—
620C2×#101—111no—
621C2×#100—111no—
622C2×#100—111no—
623C2×#100—111no—
624C2×#97—111no—
625C22×C11—22no—
626C22×C11—22no—
627C22×C11—22no—
628C22×C11—22no—
629C22×C11—42no—
630C22×C11—42no—
631C22×C11—42no—
632C22×C11—42no—
633C22×C11—42no—
634C22×C11—82no—
635C22×C11—82no—
636C22×C11—82no—
637C22×C11—82no—
638C22×C11—161no—
639C22×C11—161no—
640C22×C11—164no—
641C22×C11—164no—
642C22×C11D4211yescharacteristic
643C22×C11D4211yescharacteristic
644C22×C11C2×H(5,𝔽2)11yescharacteristic
645C2×D11—22no—
646C2×D11—42no—
647C2×D11—42no—
648C2×D11—82no—
649C2×D11—82no—
650C2×D11—164no—
651C2×D11—161no—
652C4×C11—22no—
653C4×C11—22no—
654C4×C11—22no—
655C4×C11D4211yescharacteristic
656C4×C11D4211yescharacteristic
657C4×C11C23×D411yescharacteristic
658C4×C11C23×D411yescharacteristic
659Dic11—22no—
660Dic11—42no—
661Dic11—42no—
6622−1+4—114no—
6632−1+4—222no—
6642−1+4—222no—
6652−1+4—441no—
666H(5,𝔽2)—22no—
667H(5,𝔽2)—22no—
668H(5,𝔽2)—22no—
669H(5,𝔽2)—22no—
670H(5,𝔽2)—41no—
671H(5,𝔽2)—41no—
672H(5,𝔽2)—114no—
673H(5,𝔽2)—222no—
674H(5,𝔽2)—222no—
675H(5,𝔽2)—441no—
676H(5,𝔽2)C22×D1114yes—
677H(5,𝔽2)C22×D1114yescomplemented
678C2×#41—21no—
679C2×#41—21no—
680C2×#41—21no—
681C2×#41—21no—
682C2×#41—111no—
683C2×#41—221no—
684C2×#41—221no—
685C2×#41—221no—
686C2×#41—221no—
687C2×#41—441no—
688C2×#41C22×D1111yescharacteristic
689C2×#41C22×D1111yescharacteristic
690C2×#41C22×D1111yescharacteristic
691C22×Q8—111no—
692C22×Q8—221no—
693C22×Q8—221no—
694C22×D4—21no—
695C22×D4—21no—
696C22×D4—21no—
697C22×D4—21no—
698C22×D4—41no—
699C22×D4—41no—
700C22×D4—111no—
701C22×D4—221no—
702C22×D4—221no—
703C22×D4—441no—
704C22×D4—441no—
705C22×D4C22×D1111yescharacteristic
706C22×D4C22×D1111yescharacteristic
707#137—114no—
708#137—114no—
709#137—228no—
710#137—222no—
711#137—222no—
712#137—228no—
713AGL(1,ℤ/8)—22no—
714AGL(1,ℤ/8)—22no—
715AGL(1,ℤ/8)—28no—
716AGL(1,ℤ/8)—28no—
717AGL(1,ℤ/8)—114no—
718AGL(1,ℤ/8)—114no—
719AGL(1,ℤ/8)—114no—
720AGL(1,ℤ/8)—114no—
721AGL(1,ℤ/8)—228no—
722AGL(1,ℤ/8)—228no—
723AGL(1,ℤ/8)—228no—
724AGL(1,ℤ/8)—222no—
725AGL(1,ℤ/8)—222no—
726AGL(1,ℤ/8)—222no—
727AGL(1,ℤ/8)—222no—
728AGL(1,ℤ/8)—228no—
729AGL(1,ℤ/8)C22×D1114yes—
730AGL(1,ℤ/8)C22×D1114yescomplemented
731#135—28no—
732#135—114no—
733#135—114no—
734#135—228no—
735#135—228no—
736#135—228no—
737#135C22⋊D1114yescomplemented
738#135C22×D1114yes—
739C2×Q16—111no—
740C2×Q16—221no—
741C2×Q16—221no—
742C2×Q16C22⋊D1111yescharacteristic, complemented
743C2×SD16—21no—
744C2×SD16—21no—
745C2×SD16—111no—
746C2×SD16—111no—
747C2×SD16—114no—
748C2×SD16—114no—
749C2×SD16—221no—
750C2×SD16—221no—
751C2×SD16—222no—
752C2×SD16—228no—
753C2×SD16—221no—
754C2×SD16—221no—
755C2×SD16—221no—
756C2×SD16—221no—
757C2×SD16—221no—
758C2×SD16—221no—
759C2×SD16—228no—
760C2×SD16—221no—
761C2×SD16—221no—
762C2×SD16—222no—
763C2×SD16C22⋊D1111yescharacteristic, complemented
764C2×SD16C22⋊D1111yescharacteristic, complemented
765C2×D8—21no—
766C2×D8—21no—
767C2×D8—28no—
768C2×D8—21no—
769C2×D8—21no—
770C2×D8—22no—
771C2×D8—111no—
772C2×D8—114no—
773C2×D8—221no—
774C2×D8—221no—
775C2×D8—222no—
776C2×D8—228no—
777C2×D8—221no—
778C2×D8—221no—
779C2×D8—221no—
780C2×D8—221no—
781C2×D8C22⋊D1111yescharacteristic, complemented
782C2×D8C22×D1114yescomplemented
783#131—22no—
784#131—114no—
785#131—114no—
786#131—114no—
787#131—222no—
788#131—222no—
789#131—222no—
790#131C22×D1114yescomplemented
791C2×M16—21no—
792C2×M16—111no—
793C2×M16—111no—
794C2×M16—111no—
795C2×M16—221no—
796C2×M16—221no—
797C2×M16—221no—
798C2×M16C22×D1111yescharacteristic
799C22×C8—21no—
800C22×C8—111no—
801C22×C8—221no—
802C22×C8—221no—
803C22×C8—221no—
804C22×C8C22×D1111yescharacteristic
805#127—114no—
806#127—441no—
807#124—114no—
808#124—441no—
809C2×C22⋊C4—441no—
810C2×C42—111no—
811#108—114no—
812#108—114no—
813#104—114no—
814#104—114no—
815#104—114no—
816#104—114no—
817#101—114no—
818#100—114no—
819#100—114no—
820#100—114no—
821#97—114no—
822C2×C11—21no—
823C2×C11—21no—
824C2×C11—42no—
825C2×C11—42no—
826C2×C11—42no—
827C2×C11—82no—
828C2×C11—82no—
829C2×C11#328812yescomplemented
830C2×C11C2×D4211yescharacteristic
831D11—42no—
832D11—82no—
833C24—21no—
834C24—21no—
835C24—41no—
836C24—41no—
837C24—221no—
838C24—441no—
839#41—21no—
840#41—21no—
841#41—21no—
842#41—21no—
843#41—21no—
844#41—21no—
845#41—24no—
846#41—24no—
847#41—24no—
848#41—24no—
849#41—42no—
850#41—42no—
851#41—42no—
852#41—42no—
853#41—112no—
854#41—112no—
855#41—224no—
856#41—224no—
857#41—221no—
858#41—221no—
859#41—224no—
860#41—224no—
861#41—442no—
862#41—442no—
863#41—444no—
864#41—442no—
865#41—442no—
866#41—444no—
867#41D4×D1112yes—
868#41C2×C22⋊D1112yes—
869#41C2×C22⋊D1112yes—
870#41C23×D1112yes—
871#41C23×D1112yes—
872#41C23×D1112yes—
873C2×Q8—111no—
874C2×Q8—112no—
875C2×Q8—224no—
876C2×Q8—221no—
877C2×Q8—224no—
878C2×Q8—221no—
879C2×Q8—221no—
880C2×Q8—221no—
881C2×Q8—221no—
882C2×Q8—441no—
883C2×Q8—442no—
884C2×Q8—442no—
885C2×Q8D4×D1111yescharacteristic
886C2×Q8C2×C22⋊D1111yescharacteristic
887C2×Q8C2×C22⋊D1111yescharacteristic
888C2×D4—21no—
889C2×D4—21no—
890C2×D4—21no—
891C2×D4—24no—
892C2×D4—24no—
893C2×D4—24no—
894C2×D4—24no—
895C2×D4—21no—
896C2×D4—21no—
897C2×D4—21no—
898C2×D4—21no—
899C2×D4—21no—
900C2×D4—21no—
901C2×D4—21no—
902C2×D4—21no—
903C2×D4—21no—
904C2×D4—21no—
905C2×D4—42no—
906C2×D4—42no—
907C2×D4—42no—
908C2×D4—42no—
909C2×D4—41no—
910C2×D4—41no—
911C2×D4—41no—
912C2×D4—41no—
913C2×D4—44no—
914C2×D4—44no—
915C2×D4—44no—
916C2×D4—44no—
917C2×D4—111no—
918C2×D4—112no—
919C2×D4—224no—
920C2×D4—221no—
921C2×D4—224no—
922C2×D4—221no—
923C2×D4—221no—
924C2×D4—221no—
925C2×D4—221no—
926C2×D4—221no—
927C2×D4—442no—
928C2×D4—441no—
929C2×D4—442no—
930C2×D4—441no—
931C2×D4—444no—
932C2×D4—444no—
933C2×D4—444no—
934C2×D4—441no—
935C2×D4—884no—
936C2×D4D4×D1111yescharacteristic
937C2×D4C2×C22⋊D1111yescharacteristic
938C2×D4C2×C22⋊D1111yescharacteristic
939C2×D4C23×D1112yes—
940C2×D4C23×D1112yes—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—41no—
945C22×C4—41no—
946C22×C4—221no—
947C22×C4—221no—
948C22×C4—221no—
949C22×C4—441no—
950C22×C4—441no—
951C22×C4—441no—
952C22×C4C23×D1111yescharacteristic
953Q16—114no—
954Q16—224no—
955Q16—224no—
956Q16C2×C22⋊D1114yescomplemented
957SD16—24no—
958SD16—24no—
959SD16—114no—
960SD16—114no—
961SD16—224no—
962SD16—224no—
963SD16—224no—
964SD16—224no—
965SD16—224no—
966SD16—224no—
967SD16—224no—
968SD16—224no—
969SD16—224no—
970SD16—224no—
971SD16C2×C22⋊D1114yescomplemented
972SD16C2×C22⋊D1114yescomplemented
973D8—24no—
974D8—24no—
975D8—24no—
976D8—24no—
977D8—114no—
978D8—224no—
979D8—224no—
980D8—224no—
981D8—224no—
982D8—224no—
983D8—224no—
984D8C2×C22⋊D1114yescomplemented
985M16—21no—
986M16—24no—
987M16—112no—
988M16—112no—
989M16—112no—
990M16—224no—
991M16—224no—
992M16—221no—
993M16—221no—
994M16—221no—
995M16—224no—
996M16C23×D1112yes—
997C2×C8—21no—
998C2×C8—24no—
999C2×C8—111no—
1000C2×C8—111no—
1001C2×C8—112no—
1002C2×C8—112no—
1003C2×C8—224no—
1004C2×C8—224no—
1005C2×C8—221no—
1006C2×C8—221no—
1007C2×C8—221no—
1008C2×C8—224no—
1009C2×C8C2×C22⋊D1111yescharacteristic
1010C2×C8C2×C22⋊D1111yescharacteristic
1011C2×C8C2×C22⋊D1112yes—
1012C2×C8C23×D1112yes—
1013C22⋊C4—444no—
1014C42—112no—
1015C42—221no—
1016C11C2×#328811yescharacteristic, complemented, Sylow
1017C23—21no—
1018C23—21no—
1019C23—21no—
1020C23—22no—
1021C23—22no—
1022C23—44no—
1023C23—44no—
1024C23—41no—
1025C23—41no—
1026C23—41no—
1027C23—41no—
1028C23—82no—
1029C23—82no—
1030C23—162no—
1031C23—162no—
1032C23—221no—
1033C23—222no—
1034C23—444no—
1035C23—441no—
1036C23—441no—
1037C23—882no—
1038C23—1762no—
1039C23#6703711yescharacteristic
1040Q8—21no—
1041Q8—21no—
1042Q8—21no—
1043Q8—112no—
1044Q8—221no—
1045Q8—222no—
1046Q8—222no—
1047Q8—444no—
1048Q8—441no—
1049Q8—441no—
1050Q8C2×D4×D1112yes—
1051Q8C22×C22⋊D1112yes—
1052Q8C22×C22⋊D1112yes—
1053D4—22no—
1054D4—22no—
1055D4—22no—
1056D4—22no—
1057D4—22no—
1058D4—22no—
1059D4—21no—
1060D4—21no—
1061D4—21no—
1062D4—22no—
1063D4—22no—
1064D4—22no—
1065D4—22no—
1066D4—44no—
1067D4—44no—
1068D4—44no—
1069D4—44no—
1070D4—41no—
1071D4—41no—
1072D4—41no—
1073D4—41no—
1074D4—112no—
1075D4—222no—
1076D4—222no—
1077D4—221no—
1078D4—222no—
1079D4—222no—
1080D4—444no—
1081D4—444no—
1082D4—444no—
1083D4—441no—
1084D4—441no—
1085D4—888no—
1086D4C2×D4×D1112yes—
1087D4C22×C22⋊D1112yes—
1088D4C22×C22⋊D1112yes—
1089C2×C4—21no—
1090C2×C4—21no—
1091C2×C4—21no—
1092C2×C4—22no—
1093C2×C4—22no—
1094C2×C4—22no—
1095C2×C4—22no—
1096C2×C4—22no—
1097C2×C4—22no—
1098C2×C4—44no—
1099C2×C4—44no—
1100C2×C4—221no—
1101C2×C4—222no—
1102C2×C4—222no—
1103C2×C4—222no—
1104C2×C4—222no—
1105C2×C4—444no—
1106C2×C4—444no—
1107C2×C4—444no—
1108C2×C4—442no—
1109C2×C4—441no—
1110C2×C4—441no—
1111C2×C4C2×D4×D1111yescharacteristic
1112C2×C4C2×D4×D1111yescharacteristic
1113C2×C4#6703711yescharacteristic
1114C2×C4C22×C22⋊D1111yescharacteristic
1115C2×C4C22×C22⋊D1111yescharacteristic
1116C2×C4C24×D1111yescharacteristic
1117C8—22no—
1118C8—112no—
1119C8—112no—
1120C8—222no—
1121C8—222no—
1122C8—222no—
1123C8C22×C22⋊D1112yes—
1124C8C22×C22⋊D1112yes—
1125C22—22no—
1126C22—22no—
1127C22—22no—
1128C22—22no—
1129C22—42no—
1130C22—42no—
1131C22—42no—
1132C22—42no—
1133C22—42no—
1134C22—82no—
1135C22—82no—
1136C22—82no—
1137C22—82no—
1138C22—161no—
1139C22—161no—
1140C22—164no—
1141C22—164no—
1142C22—222no—
1143C22—442no—
1144C22—442no—
1145C22—882no—
1146C22—882no—
1147C22—1761no—
1148C22—1764no—
1149C22D4×C22⋊D1111yescharacteristic
1150C22D4×C22⋊D1111yescharacteristic
1151C22C2×#6703711yescharacteristic
1152C4—22no—
1153C4—22no—
1154C4—22no—
1155C4—222no—
1156C4—442no—
1157C4—442no—
1158C4D4×C22⋊D1111yescharacteristic
1159C4D4×C22⋊D1111yescharacteristic
1160C4C22×D4×D1111yescharacteristic
1161C4C23×C22⋊D1111yescharacteristic
1162C2—21no—
1163C2—21no—
1164C2—42no—
1165C2—42no—
1166C2—42no—
1167C2—82no—
1168C2—82no—
1169C2—442no—
1170C2—882no—
1171C2#1308038012yesdirect product factor
1172C2C2×D4×C22⋊D1111yescharacteristic
subgroupG/H
centerC22D4×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#576C2
socleC22×C11D42
hypercenterC2×#576D11
hypocenterC11C2×#3288
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#576

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#10623367C2semidirect
2. C2×#10623301C2semidirect
3. C2×#10623366C2semidirect
4. #13080380C2direct (N × H)
5. C2×#10622767C2semidirect
6. C2×#10622812C2semidirect
7. C2×#10622773C2semidirect
8. C2×#10622754C2semidirect
9. C2×#10622813C2semidirect
10. C2×#10622814C2semidirect
11. C2×#10622855C2semidirect
12. C2×#10622854C2semidirect
13. C2×#10622811C2semidirect
14. C2×#10622810C2semidirect
15. C2×#10622758C2semidirect
16. C2×C11×#576C2semidirect
18. C2×C11×H(5,𝔽2)C22semidirect
19. C2×#67043C22semidirect
20. C2×#67042C22semidirect
22. C11×#576C22semidirect
26. C2×C11×AGL(1,ℤ/8)C22semidirect
30. C22×C11×D8C22semidirect
31. C2×C11×#131C22semidirect
33. #10623367C22semidirect
35. #10623366C22semidirect
37. C2×#67004C22semidirect
38. C2×#67004C22semidirect
44. C2×#67002C22semidirect
45. C2×#67001C22semidirect
46. C2×#67001C22semidirect
47. C2×#66993C22semidirect
48. C2×#66989C22semidirect
50. C22×#4324C22semidirect
53. C2×#66985C22semidirect
54. C2×#66985C22semidirect
56. C22×#4323C22semidirect
58. #10623301C22semidirect
63. C22×#4314C22semidirect
64. C2×#66954C22semidirect
65. #10622855C22semidirect
66. #10622854C22semidirect
67. C2×#66901C22semidirect
68. C2×#66901C22semidirect
69. C2×#66901C22semidirect
70. C2×#66897C22semidirect
71. C2×#66897C22semidirect
72. #10622814C22semidirect
73. #10622813C22semidirect
74. #10622812C22semidirect
75. #10622811C22semidirect
76. #10622810C22semidirect
77. #10622773C22semidirect
78. #10622767C22semidirect
79. #10622758C22semidirect
80. #10622754C22semidirect
81. C2×#66889C22semidirect
82. C2×#66888C22semidirect
83. C2×#66887C22semidirect
84. C2×#66886C22semidirect
85. C2×#66883C22semidirect
86. C2×#66879C22semidirect
94. C11×H(5,𝔽2)C23semidirect
114. #67043C23semidirect
118. #67042C23semidirect
137. C11×AGL(1,ℤ/8)C23semidirect
139. C11×#135D4semidirect
141. C2×C11×Q16D4semidirect
144. C2×C11×SD16D4semidirect
145. C2×C11×SD16D4semidirect
152. C2×C11×D8D4semidirect
153. C2×C11×D8C23semidirect
155. C11×#131C23semidirect
164. #67004C23semidirect
165. #67004C23semidirect
168. #67003D4semidirect
174. #67002C23semidirect
177. #67001C23semidirect
178. #67001C23semidirect
181. C2×#4326D4semidirect
184. C2×#4325D4semidirect
186. #66993C23semidirect
188. #66989C23semidirect
197. C2×#4324D4semidirect
198. C2×#4324C23semidirect
203. #66985C23semidirect
204. #66985C23semidirect
213. C2×#4323D4semidirect
214. C2×#4323C23semidirect
231. C2×#4314C23semidirect
233. #66954C23semidirect
236. #66901C23semidirect
237. #66901C23semidirect
238. #66901C23semidirect
239. #66897C23semidirect
240. #66897C23semidirect
241. #66889C23semidirect
242. #66888C23semidirect
243. #66887C23semidirect
244. #66886C23semidirect
245. #66883C23semidirect
246. #66879C23semidirect
368. C11×Q16C2×D4semidirect
371. C11×SD16C2×D4semidirect
372. C11×SD16C2×D4semidirect
377. C11×D8C2×D4semidirect
390. #4326C2×D4semidirect
393. #4325C2×D4semidirect
400. #4324C2×D4semidirect
407. #4323C2×D4semidirect
434. C2×#576D11semidirect
558. C2×H(5,𝔽2)C2×D11semidirect
566. #576C2×D11semidirect
582. C2×AGL(1,ℤ/8)C2×D11semidirect
596. C22×D8C2×D11semidirect
600. C2×#131C2×D11semidirect
677. H(5,𝔽2)C22×D11semidirect
730. AGL(1,ℤ/8)C22×D11semidirect
737. #135C22⋊D11semidirect
742. C2×Q16C22⋊D11semidirect
763. C2×SD16C22⋊D11semidirect
764. C2×SD16C22⋊D11semidirect
781. C2×D8C22⋊D11semidirect
782. C2×D8C22×D11semidirect
790. #131C22×D11semidirect
829. C2×C11#3288semidirect
956. Q16C2×C22⋊D11semidirect
971. SD16C2×C22⋊D11semidirect
972. SD16C2×C22⋊D11semidirect
984. D8C2×C22⋊D11semidirect
1016. C11C2×#3288semidirect
1171. C2#13080380direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#106233672
C2×#106233012
C2×#106233662
#130803802
C2×#106227672
C2×#106228122
C2×#106227732
C2×#106227542
C2×#106228132
C2×#106228142
C2×#106228552
C2×#106228542
C2×#106228112
C2×#106228102
C2×#106227582
C2×C11×#5762
C2×#328811